Solve {l}{(5/7)^{-2}*(7/5)^-3}{(3^3/2^2)^2}

$$\left. \begin{array}{l}{ ( \frac { 5 } { 7 } ) ^ { - 2 } \cdot ( \frac { 7 } { 5 } ) ^ { - 3 } }\\{ ( \frac { 3 ^ { 3 } } { 2 ^ { 2 } } ) ^ { 2 } }\end{array} \right.$$

Sort

$$\frac{5}{7},\ \frac{729}{16}$$

Solution Steps

Calculate \frac{5}{7} to the power of -2 and get \frac{49}{25}.

$$sort(\frac{49}{25}\times \left(\frac{7}{5}\right)^{-3},\left(\frac{3^{3}}{2^{2}}\right)^{2})$$

Calculate \frac{7}{5} to the power of -3 and get \frac{125}{343}.

$$sort(\frac{49}{25}\times \frac{125}{343},\left(\frac{3^{3}}{2^{2}}\right)^{2})$$

Multiply \frac{49}{25} and \frac{125}{343} to get \frac{5}{7}.

$$sort(\frac{5}{7},\left(\frac{3^{3}}{2^{2}}\right)^{2})$$

Calculate 3 to the power of 3 and get 27.

$$sort(\frac{5}{7},\left(\frac{27}{2^{2}}\right)^{2})$$

Calculate 2 to the power of 2 and get 4.

$$sort(\frac{5}{7},\left(\frac{27}{4}\right)^{2})$$

Calculate \frac{27}{4} to the power of 2 and get \frac{729}{16}.

$$sort(\frac{5}{7},\frac{729}{16})$$

Least common denominator of the numbers in the list \frac{5}{7},\frac{729}{16} is 112. Convert numbers in the list to fractions with denominator 112.

$$\frac{80}{112},\frac{5103}{112}$$

Evaluate

$$\frac{5}{7},\ \frac{729}{16}$$